Preparations

Load the necessary libraries

library(car) # for regression diagnostics
library(broom) # for tidy output
library(broom.mixed) # for tidy output
library(ggfortify) # for model diagnostics
library(sjPlot) # for outputs
library(knitr) # for kable
library(effects) # for partial effects plots
library(ggeffects) # for effects plots in ggplotjk
library(emmeans) # for estimating marginal means
library(MASS) # for glm.nb
library(MuMIn) # for AICc
library(tidyverse) # for data wrangling
library(DHARMa) # for assessing dispersion etc
library(glmmTMB) # for glmmTMB
library(performance) # for diagnostic plots
library(see) # for diagnostic plots
library(lme4) # for glmer
library(glmmTMB) # for glmmTMB

Scenario

Some ornithologists were interested in the degree of sibling negotiations in owl chicks. Specifically, they wanted to explore how sibling negotiations were affected by feeding satiety and the sex of the parent returning to the nest. The ornithologists had accessed to a number of owl nests and were able to count (via recording equipment) the number of sibling negotiations (calls) that the owl chicks made when the parent returned to the nest.

We could hypothesise that the chicks might call more if they were hungry. As part of the investigation, the researchers were able to provided supplementary food. As such, they were able to manipulate the conditions such that sometimes the chicks in a nest would be considered deprived of supplementary food and at other times they were satiated.

As a parent returned, the researchers recorded the number of sibling negotiations (calls) along with the sex of the parent. Since the number of calls is likely to be a function of the number of chicks (the more chicks the more calls), the researchers also counted the number of siblings in the brood.

Each nest was measured on multiple occasions. Hence, we must include the nest as a random effect to account for the lack of independence between observations on the same set of siblings.

Read in the data

owls <- read_csv("../public/data/owls.csv", trim_ws = TRUE)
glimpse(owls)
## Rows: 599
## Columns: 7
## $ Nest               <chr> "AutavauxTV", "AutavauxTV", "AutavauxTV", "Autavaux…
## $ FoodTreatment      <chr> "Deprived", "Satiated", "Deprived", "Deprived", "De…
## $ SexParent          <chr> "Male", "Male", "Male", "Male", "Male", "Male", "Ma…
## $ ArrivalTime        <dbl> 22.25, 22.38, 22.53, 22.56, 22.61, 22.65, 22.76, 22…
## $ SiblingNegotiation <dbl> 4, 0, 2, 2, 2, 2, 18, 4, 18, 0, 0, 3, 0, 3, 3, 6, 0…
## $ BroodSize          <dbl> 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, …
## $ NegPerChick        <dbl> 0.8, 0.0, 0.4, 0.4, 0.4, 0.4, 3.6, 0.8, 3.6, 0.0, 0…

Data preparation

Exploratory data analysis

Model formula: \[ y_i \sim{} \mathcal{Pois}(\lambda_i)\\ ln(\lambda_i) =\boldsymbol{\beta} \bf{X_i} + \boldsymbol{\gamma} \bf{Z_i} \]

where \(\boldsymbol{\beta}\) and \(\boldsymbol{\gamma}\) are vectors of the fixed and random effects parameters respectively and \(\bf{X}\) is the model matrix representing the overall intercept and effects of food treatment, sex of parent, arrival time (and various interactions) on the number of sibling negotiations. Brood size was also incorporated as an offset. \(\bf{Z}\) represents a cell means model matrix for the random intercepts associated with individual nests.

Fit the model

Model validation

Model refit and validation

Partial plots

Model investigation / hypothesis testing

Predictions

Summary figures

References